I didn't find anything about this topic specifically on search, so I'll give it a try.
http://en.wikipedia.org/wiki/Heinkel_He_177
Historically the He-177 heavy bomber had several notorious problems, mostly to do with its engines, as it was produced as a two propeller aircraft with dual-linked engines for each, mostly to facilitate its dive bombing capabilities. Even with Goering cancelling the heavy bomber project in 1937 (really cancelled by Wever before his death in 1936, because the models presented were too costly), the He-177 was approved in 1938, but only if it were redesigned as a heavy dive bomber. This delayed the aircraft until 1942 and it suffered from major problems for he rest of the war, despite being produced in approximately 1000 units. It was never built as a 4 engine bomber outside of some test units that were mostly destroyed in allied bombing raids. Most researchers seem to agree that a simple four engine, four propeller set up would have made it an excellent aircraft on par with the B-17 and made it available in 1940.
So what if the dive bombing requirement was not made on this bomber and it continued its normal development path, with the first units becoming available in mid-1940? The navy had orders for units as well as the Luftwaffe, which the Condor was used to fill because the Griffin wasn't available on time, so it was very likely to have appeared in place of the Condor, or at least side-by-side with it. Obviously the units would not be really ready for operational bombing or recon work until 1941 thanks to training for both ground and air crews, as well as practice in tactics for what would be the first heavy bomber in the German arsenal. Historically it was ultimately produced in large numbers, more than 1000 over the course of the war, and this would actually be likely higher if it were more reliable. The BoB and Blitz would be over before it could be useful over Britain and even if it were used, it wouldn't likely have made a major difference thanks to smaller initial numbers, unfamiliarity with the tactics necessary for truly effective bombing, and the fact that medium bombers were enough for major damage anyway and didn't achieve anything of value.
Its more likely to see major use over Russia and to more effect. They could strike at Russian factories in the Urals and power plants, which were really the achillies heel that needed to be hit.
Perhaps something like this?:
http://en.wikipedia.org/wiki/Operation_Eisenhammer
A bit about the technical issues:
"
The mock-up was completed in November 1937, and on November 5, 1937 allocated the official RLM type number "8-177", the same day that the Luftwaffe High Command (OKL) first stipulated the requirement for the new design to possess sufficient structural strength to enable it to undertake medium degree diving attacks."
Part of the He-177's problem was the redesign took about 24 months, meaning the first prototypes of the of the dive bombing He-177 weren't around until November 1939 or so.
"
On November 9, 1939, the first prototype, the He 177 V1 was flown for the first time with Leutnant Carl Francke, Dipl. Ing., chief of the Rechlin flight test center, at the controls. The initial flight terminated abruptly after only twelve minutes as a result of overheating engines."
So the prototype was setback by 2 years, meaning all the time for practical experience in correcting the airframe or whatever, was setback and the aircraft was burdened with a much worse design that it wasn't originally created to handle. The lost two years would have been plenty to correct much of any basic design flaws, especially because those corrections wouldn't have been as major as what was applied for the dive bombing requirements.
"
The initial production version of the Greif, the He 177 A-1, demonstrated a tendency for instability in the yaw and pitch axes during August 1942, during flight tests, that would have led to poor bombing accuracy in action. Shortly after these tests, the third production A-1 example (factory serial number 15153, with Stammkennzeichen of GI + BN) had its fuselage lengthened by 160 cm (63 in) just aft of the trailing edge of the wing, and tests of the modified aircraft, from the longer distance of the "tail moment" that resulted, gave a marked degree of improvement in the yaw and pitch axis stability, enough to mandate the construction of the He 177 A-3 and all later models of the He 177 with the lengthened fuselage"
Looks like the early problems were easy to fix, other than the OTL engine problems. Other problems existed, but the fixes were relatively easy if the engine problem didn't need to be tackled.